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Privacy Preservation in MIMO-OFDM Localization Systems: A Beamforming Approach

Yuchen Zhang, Hui Chen, Musa Furkan Keskin, Alireza Pourafzal, Pinjun Zheng, Henk Wymeersch, Tareq Y. Al-Naffouri

TL;DR

This work tackles location privacy in uplink MIMO-OFDM localization by considering a legitimate BS and an eavesdropping BS. It introduces a CRB-based beamforming optimization that minimizes $CRB_{B}(p_A)$ while enforcing $CRB_{E}(p_A) \ge \gamma$, solved via a matrix lifting and Penalty Dual Decomposition (PDD) approach that alternates SDP subproblems. The method introduces lifted variables $V=WW^H$, an auxiliary $U$, and a privacy-enforcing $\Phi$, yielding an augmented Lagrangian with inner BCD steps. Numerical results show the proposed scheme outperforms two power-control benchmarks, maintaining full transmit power while suppressing Eve’s localization capability, highlighting its practical value for privacy-aware 6G localization.

Abstract

We investigate an uplink MIMO-OFDM localization scenario where a legitimate base station (BS) aims to localize a user equipment (UE) using pilot signals transmitted by the UE, while an unauthorized BS attempts to localize the UE by eavesdropping on these pilots, posing a risk to the UE's location privacy. To enhance legitimate localization performance while protecting the UE's privacy, we formulate an optimization problem regarding the beamformers at the UE, aiming to minimize the Cramér-Rao bound (CRB) for legitimate localization while constraining the CRB for unauthorized localization above a threshold. A penalty dual decomposition optimization framework is employed to solve the problem, leading to a novel beamforming approach for location privacy preservation. Numerical results confirm the effectiveness of the proposed approach and demonstrate its superiority over existing benchmarks.

Privacy Preservation in MIMO-OFDM Localization Systems: A Beamforming Approach

TL;DR

This work tackles location privacy in uplink MIMO-OFDM localization by considering a legitimate BS and an eavesdropping BS. It introduces a CRB-based beamforming optimization that minimizes while enforcing , solved via a matrix lifting and Penalty Dual Decomposition (PDD) approach that alternates SDP subproblems. The method introduces lifted variables , an auxiliary , and a privacy-enforcing , yielding an augmented Lagrangian with inner BCD steps. Numerical results show the proposed scheme outperforms two power-control benchmarks, maintaining full transmit power while suppressing Eve’s localization capability, highlighting its practical value for privacy-aware 6G localization.

Abstract

We investigate an uplink MIMO-OFDM localization scenario where a legitimate base station (BS) aims to localize a user equipment (UE) using pilot signals transmitted by the UE, while an unauthorized BS attempts to localize the UE by eavesdropping on these pilots, posing a risk to the UE's location privacy. To enhance legitimate localization performance while protecting the UE's privacy, we formulate an optimization problem regarding the beamformers at the UE, aiming to minimize the Cramér-Rao bound (CRB) for legitimate localization while constraining the CRB for unauthorized localization above a threshold. A penalty dual decomposition optimization framework is employed to solve the problem, leading to a novel beamforming approach for location privacy preservation. Numerical results confirm the effectiveness of the proposed approach and demonstrate its superiority over existing benchmarks.
Paper Structure (18 sections, 13 equations, 3 figures, 1 algorithm)

This paper contains 18 sections, 13 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model And Problem Formulation
  3. Signal Model
  4. CRB-Based Performance Metric
  5. Problem Formulation
  6. PDD-Based Beamforming for location privacy Preservation
  7. Problem Reformulation
  8. PDD-Based Optimization Framework
  9. Augmented Lagrangian Problem
  10. Solving ALP with BCD
  11. Convergence and Complexity
  12. Numerical Results
  13. Scenarios
  14. Benchmarks
  15. Results and Discussion
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Illustration of the risk of location privacy leakage in a MIMO OFDM localization system with coexisting legitimate and unauthorized nodes.
  • Figure 2: Beampatterns under different location privacy constraint: (a) $\sqrt{\gamma} = 0\text{ m}$; (b) $\sqrt{\gamma} = 1\text{ m}$; (c) $\sqrt{\gamma} = 4\text{ m}$; (d) $\sqrt{\gamma} = 10\text{ m}$.
  • Figure 3: Comparison between the proposed scheme and benchmarks: (a) $\sqrt{\text{CRB}}$ at Bob versus $\sqrt{\gamma}$; (b) Allowable transmit power versus $\sqrt{\gamma}$.